Kinetic Theory and Fluid Dynamics

By Y. Sone, C. Michaelis. 2002

616 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/26345aa02a89bc001e0ab871b4e695a58c0895b1

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Citations in the corpus

Mathematical tools for kinetic equations (2004, background): “For physical motivations and mathematical properties one can consult Truesdell and Muncaster [113], Cercignani [32], and Sone [111].”
Constructive methods of invariant manifolds for kinetic problems (2003, methodology): “The Hilbert method is not very popular now, nevertheless, for some purposes it may be more convenient than the Chapman–Enskog method, for example, for a studying of stationary solutions [218].”
Multiple-relaxation-time lattice Boltzmann model for the convection and anisotropic diffusion equation (2010, methodology): “) Diffusive scaling was first developed by Sone [53] to explain the connection between the Boltzmann equation and fluid-dynamic systems [54,55] and was later applied to the LBE to prove that the numerical solution converges to the incompressible Navier–Stokes equation [49,50,56].”
A lattice Boltzmann method for incompressible two-phase flows with large density differences (2004, background): “where f c i and g c i are functions of Chapman–Enskog type in which the variables x and t enter only through macroscopic variables and/or their derivatives [22], sf and sg are dimensionless single relaxation times, Dx is a spacing of the cubic lattice, Dt is a time step during which the particles tr”
A Review on the development of lattice Boltzmann computation of macro fluid flows and heat transfer (2015, background): “As a great number of such model equations like the Navier–Stokes equations do not possess analytical solutions, one has to resort to numerical methods [2].”
Asymptotic analysis of the lattice Boltzmann equation (2005, methodology): “The diffusive scaling, developed by Sone (cf. [43]), is well known in kinetic theory and has been used to establish a direct connection between the Boltzmann equation and the incompressible Navier–Stokes equations [9] [1] [29] [14] [15].”
Continuum limit of self-driven particles with orientation interaction (2007, background): “The reader can refer to [8, 11, 31] for recent viewpoints as well as to [6, 15, 37] for major landmarks in its mathematical theory.”
A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources (2009, background): “However, for physical boundary conditions, as Maxwell diffusive conditions, boundary layers will be generated where the solution is very far away from Gaussian distributions [55].”